First I will say great work on the rules and the background fluff in the PDF.

I do have what may be a dumb question, but I’ll ask it anyway, just to be sure.
While reading the (PDF) manual, I got confused by the term “next Maintenance Phase”.
Specifically - whether it refers to the first occurrence of the Maintenance Phase ( after whatever action triggered it ), or if it refers to the Maintenance Phase following the next turn.

My confusion comes from the english language use of “next”. For example - if I say “let’s meet on Saturday” verses “let’s meet Next Saturday”? Is it clear they mean the same day, or a week apart.

In the manual there are several examples where “next” is used, and other examples where the rules clearly specifies it is the Maintenance Phase of that turn being referred to.

Some examples from the PDF:
If Bill Psyches goes last and stuns someone - do they recover immediately or remain stunned for the following activation ( due to Maintenance Phase pages 14 and 27 ) ? First case is unclear ( to me ) while the second case is Yes.
Of if an Urkin lobs a Smoke Grenade on the last turn - does it dissipate immediately (in Maintenance Phase ) and provide no Line of Sight Cover next turn ( page 141 )?

Fair question (certainly not dumb!) as the English language can be confusing as you say.

After reading over the examples you point to I think "next Maintenance Phase" refers to the maintenance phase of the current turn. Literally the very next maintenance phase you encounter.

So yes, lobbing a smoke grenade as the final action of an activation phase would be useless, and you would feel unlucky to stun someone at that time. Both effects are wiped clean from the table in the maintenance phase of this turn.

I guess this points to some strategic thought needed each turn. If you want smoke to provide cover you need to put that character at the front of your activation deck...you can't rely on the smoke lasting for multiple turns.